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The probability of a car passing a certain intersection in a 20 minute windows is 0.9. What is the probability of a car passing the intersection in a 5 minute window? (Assuming a constant probability throughout.)
Let $x$ be the probability of a car passing the intersection in a 5 minute window. The probability of a car passing in a 20 minute window is equal to 1 – (probability of no car passing in a 20 minute window). The probability of a car passing in a 20 minute window is equal to 1 – (1 – probability of a car passing in a 5 minute window)$^4$. Hence: \begin{align} 0.9 &= 1 – (1 – x)^4\\ (1 – x)^4 &= 0.1\\ 1 – x &= 10^(0.25)\\ x &= 1 – 10^(0.25)\\ &= 0.4377 \end{align}